10/23/2006 Stefan Ballmer, Caltech G Stochastic Background of Gravitational Waves For the stochastic analysis group Stefan Ballmer California Institute of Technology Limits on a

10/23/2006 Stefan Ballmer, Caltech G Outline i. Introduction ii. Isotropic background search iii. Anisotropic background (directional) search iv. Other activities: i.Hanford 4km + 2km search ii.Hanford 4km + 2km high frequency (37.5kHz) search iii.ALLEGRO + Ligo Livingston search

10/23/2006 Stefan Ballmer, Caltech G Introduction The Gravitational Wave background can be l Isotropic (i.e. only small anisotropies)  Primordial origin (e.g. inflation)  Astrophysical origin, from many weak sources l Anisotropic  Astrophysical origin, from fewer strong sources Wave form unknown, but signal always present l Analysis method:  Cross-correlation between two detectors

10/23/2006 Stefan Ballmer, Caltech G l Energy density: l Characterized by log- frequency spectrum: l Related to the strain power spectrum: l Strain scale: Isotropic Background of Gravitational Waves

10/23/2006 Stefan Ballmer, Caltech G Detection Strategy, isotropic For template: Choose N such that: Overlap Reduction Function l Cross-correlation estimator l Theoretical variance l Optimal Filter

10/23/2006 Stefan Ballmer, Caltech G Landscape Cosmic Strings models and Pre-Big- Bang models: - can easily escape other experimental bounds - accessible to LIGO. 6.5 × 10 -5

10/23/2006 Stefan Ballmer, Caltech G S5 Status (1) l Online analysis:  Quick feedback  No data-quality cuts, calibration not up to date… l First pass at H1L1:  Time-shift: defining cuts blindly.  Calibration available: Nov 5, 2005 – Apr 3,  32 Hz high-pass filter, in order to push analysis down to 40 Hz.  Several lines correlated between H1 and L1: –48.0 Hz, –108.9 Hz (simulated pulsar), – Hz, –193.7 Hz (simulated pulsar) Coh = CSD 2 / PSD 1 / PSD 2

10/23/2006 Stefan Ballmer, Caltech G S5 Status (2) l Flat spectrum, H 0 = 72 km/s/Mpc: σ Ω = 1.67 ×  2.5× better than S4, but still weaker than the BBN bound (~1.1 × in our frequency band). Running Point Estimate Theoretical Standard Deviation Time-shift ~ 1-sec

10/23/2006 Stefan Ballmer, Caltech G l Stochastic GW Background due to Astrophysical Sources?  Not isotropic if dominated by nearby sources  Do a Directional Stochastic Search l Source position information from  Signal time delay between different sites (sidereal time dependent)  Sidereal variation of the single detector acceptance  Time-Shift and Cross-Correlate! Directional search motivation

10/23/2006 Stefan Ballmer, Caltech G l Cross-correlation estimator l Theoretical variance l Optimal Filter Strain Power: Choose N such that: Detection Strategy, point source Point Spread Function

10/23/2006 Stefan Ballmer, Caltech G S4 Upper Limit map, H(f)=const

10/23/2006 Stefan Ballmer, Caltech G S4 Upper Limit map, H(f)~f -3

10/23/2006 Stefan Ballmer, Caltech G Application: Low-Mass X-ray Binary (LMXB) l Accretion driven pulsars  Spun up to 300Hz <f spin <730Hz  Torque balanced by GW? –Likely for B<< Gauss l From torque balance: l Sco-X1:  Is brightest X-ray source in sky  Low magnetic field (~10 7 Gauss)  Spin frequency unknown (Artist’s impression: NASA)

10/23/2006 Stefan Ballmer, Caltech G Frequency dependent Strain Upper Limit Sco-X1 Strain (RMS)

10/23/2006 Stefan Ballmer, Caltech G Other activities l Deconvolution of maps  Use maximum likelihood estimator to reduce PSF l Hanford 4km & 2km analysis  Environmental sources that explain excess coherence identified l High frequency (37.5kHz) analysis  Exploit interferometer sensitivity at the 1 st free spectral range l Livingston – ALLEGRO (GW bar at LSU) analysis  has decent sensitivity around 915Hz (Strain ~ Hz -1/2)  40km from LIGO Livingston (Overlap Reduction Function close to 1) l LIGO-VIRGO  Working on code compatibility for future collaboration

10/23/2006 Stefan Ballmer, Caltech G Background material l Method paper  Allen, Romano, PRD (1999) l Most recent paper:  Isotropic upper limit, S4, submitted to in ApJ: l Thesis  Directional search, Stefan Ballmer, MIT, (Ph.D).:  H1-H2 low frequency search Nickolas Fotopoulos, MIT, (M.S.):

10/23/2006 Stefan Ballmer, Caltech G The